A sticky-fingered ex-con was busted after he allegedly snatched a $225,000 painting by famed expressionist Franz Kline from a tony Manhattan art gallery, The Post has learned.

Calvin Gonzalez, 46, who has several prior arrests that include grand larceny and drug possession, waltzed into the Marianne Boesky Gallery on West 24th Street in Chelsea at about 4:35 p.m. on May 12, cops said.

For about 20 minutes, he browsed works by Italian-American Salvatore Scarpitta, whose wrap paintings were being showcased in an exhibit, police sources said.

Scarpitta’s work was featured with such contemporaries as Kline, Matthew Barney and Jeff Koons.

He was also affiliated with a group called the Monument Men, who helped to recover art stolen by the Nazis.

After zeroing in on Kline’s “Black Ink,” Gonzalez allegedly grabbed it off a wall, stuffed it into a bag, and brazenly walked out of the gallery.

The staff realized the painting was gone only when it was too late, and then notified police, sources said.

With the help of surveillance video from the gallery, detectives were able to identify Gonzalez, and arrested him Saturday for felony grand larceny.

Gonzalez, who has served two stints in prison on drug-related charges, is being held without bail on Rikers Island.

The gallery declined to comment.

Security appeared lax there yesterday, as a handful of employees milled around without paying attention to a Post reporter and a few customers looking at artwork.

Kline, who died in 1962 of heart disease, was an American painter primarily associated with the abstract-expressionist movement.